A Phase-Field Method for Dynamic Ductile Fracture with Lie-Group-Preserving Remeshing

Abstract

The phase-field model for fracture is well established as a versatile tool for simulating complex crack patterns, particularly in brittle materials. Its application to ductile materials, however, remains more limited. Even less studied is the interaction between shear bands, a distinct failure mechanism, and phase-field fracture. Under high-rate loading, shear bands are characterized by extreme plastic deformation, thermal softening, and intense strain localization, posing significant computational challenges including severe mesh distortion. Existing phase-field formulations for ductile fracture have primarily been validated under non-localized plasticity, where deformation is moderate and strain gradients remain mild. Their applicability to shear-band-dominated, high-rate loading conditions remains largely unexplored.This dissertation addresses the gap in modeling ductile fracture under high-rate loading conditions in shear-band-dominated regimes. First, a variational thermo-elastic-viscoplastic phase-field framework is developed for ductile fracture under high-rate loading. The model adopts an Elastic-Plastic-Plastic Damage (EPPD) formulation, in which both elastic and plastic strain energies contribute to damage evolution, and embeds the Johnson-Cook constitutive model within a thermodynamically consistent framework. A coalescence function degrades the fracture toughness to control crack propagation direction. In shear-band-dominated regimes, plastic energy is shown to be essential to the crack driving force, as elastic energy alone is insufficient when plastic dissipation exceeds stored elastic energy by several orders of magnitude.Second, mesh-converged simulations are demonstrated within a coupled thermo-mechanical finite element framework. Mesh convergence is shown to depend critically on thermal diffusion and rate-dependent plasticity. Resolution requirements relative to shear band width are quantified for both a "tophat" problem and a three-dimensional hollow-cylinder torsion experiment, with convergence demonstrated in shear band thickness and peak effective plastic strain.Third, a Lie-group-preserving remeshing and mapping strategy is implemented to enable simulations beyond shear band localization. By mapping tensor-valued state variables to their corresponding Lie algebras prior to interpolation, the method preserves physical constraints such as the isochoricity of the plastic deformation gradient. The remeshing workflow, coordinating MOOSE, CUBIT, and SIERRA, is validated through increasingly complex problems, demonstrating that remeshing is a prerequisite, not merely a numerical convenience, for evaluating phase-field damage models under extreme shear deformation. Finally, a triaxiality-dependent damage model is assessed, revealing qualitatively different crack path predictions in low-triaxiality, shear-dominated regimes and identifying open questions for model validation. Together, these contributions establish a computational framework for simulating ductile fracture under extreme shear deformation.